(untitled) (Contemporary Mathematics, 2025)
This paper investigates the recovery of optical soliton solutions for the concatenation model, incorporating fractional temporal evolution while excluding self-phase modulation effects. To achieve this, we employ the enhanced direct algebraic method and the new projective Riccati equation approach, both of which prove effective in extracting a comprehensive spectrum of optical soliton solutions. The obtained soliton families include bright solitons, dark solitons, singular solitons, and straddled soliton structures, each characterized by distinct parameter constraints. Additionally, the impact of fractional temporal evolution on soliton behavior is analyzed, revealing how variations in the fractional order influence soliton amplitude, width, and stability. The derived parameter conditions governing the existence of these solitons provide deeper insight into the dynamics of optical pulse propagation in nonlinear media. These findings contribute to a broader understanding of soliton behavior in optical fiber systems and may offer potential applications in fiber-optic communication and photonic signal processing.